This chapter explores the theory of supply chain intermediation. Using a bargaining theoretic framework, we set out to examine why intermediaries exist, different forms they operate, and the way they inﬂuence supply chain efﬁciency. The notion of intermediary has its root in the economics literature, referring to those economic agents who coordinate and arbitrate transactions in between a group of suppliers and customers. Distinctions are often drawn between a “market maker” and a “broker” intermediary Resnick et al., 1998. The former buys, sells, and holds inventory (e.g., retailers, wholesales), while the latter provides services without owning the goods being transacted (e.g., insurance agents, ﬁnancial brokage). Sarkar et al. (1995) offer a list of various intermediation services. They distinguish the services that beneﬁt the customers (e.g. assistance in search and evaluation, needs assessment and product matching, risk reduction, and product distribution/delivery) and those that beneﬁt the suppliers (e.g. creating and disseminating product information). Taking a step further, Spulber (1996) views intermediary as the fundamental building

∗ S.

David Wu is supported by NSF Grants DMI-0075391 and DMI-0121395

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block of economic activities. He proposes the intermediation theory of the ﬁrm which suggests that the very existence of ﬁrms is due to the needs for intermediated exchange between a group of suppliers and customers. A ﬁrm is created when “the gains from intermediated exchange exceed the gains from direct exchange (between the supplier and the customer).” He also suggests that “with intermediated exchange, ﬁrms select prices, clear markets, allocate resources, and coordinate transactions.” By this deﬁnition, ﬁrms are intermediaries which establish and operate markets. Much of the earlier debate regarding the social/economic impact of Internet surrounds the possible “disintermediation” of traditional entities (c.f., Wigand and Benjamin 1996 ) and the formation of new intermediaries Kalakota and Whinston, 1997; Bollier, 1996. Disintermediation occur when an intermediary is removed from a transaction. The term was ﬁrst used with regard to the ﬁnancial services industry in the late 1960’s to describe the trend for small investors to invest directly in ﬁnancial instruments such as money market funds rather than through the traditional intermediary, a bank savings account Gellman, 1996. Popular discussions suggest that efﬁciencies in B2B e-commerce are obtained by disintermediation: that is, by cutting out “middlemen” and supplanting presumably costly intermediaries with direct transactions between the suppliers and buyers Hoffman, 1995; Imparato and Harari, 1995; Schiller and Zellner, 1994. On the other side of the debate, Fox (1999), Lu (1997a; 1997b), Crowston (1996), and Sarkar et al. (1995) show that intermediaries are still essential in electronic commerce, and argue that only the form of intermediation changes (reintermediation). Bailey (1998) suggests that both intermediation and disintermediation hypotheses are correct under different circumstances. He considers three basic transaction structures: disintermediated (direct exchange), market (where each intermediary carries all products from all suppliers, and the consumer only needs to visit one intermediary for these products), hierarchy (where each supplier chooses exactly one intermediary as in a distribution channel, and the consumer must choose among all intermediaries for different products). He shows that the preferred market structure to minimize transaction costs dependents on the number of suppliers. If the number is very small, a disintermediated market is preferred. As the number of suppliers increases, the market is preferred. After a point when the suppliers become numerous, the hierarchy is preferred. The economics literature in market intermediation, agency theory, and bargaining theory offer rich and solid foundations for the study of intermediaries and their role in the supply chain. Spulber (1999) proposed the intermediary theory as a means to understanding market microstructure. The theory offers powerful explanation for why intermediaries exist, their advantage over direct exchange, and their roles in price setting, transaction costs, and the nature of competition. He suggests that markets reach equilibrium through strate-

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gic pricing and contracting by intermediaries. Intermediaries serve the critical functions of reducing transaction costs, pooling and diversifying risk, lowering costs of matching and searching, and alleviating adverse selection. Financial market literature also offers signiﬁcant insights in the role of intermediation and market design. Campbell, et al. (1999) provides a comprehensive survey on the econometrics of ﬁnancial markets. O’Hara (1995), and Frankel et al. (1996) offer signiﬁcant insights of the theory of ﬁnancial market microstructures. Harker and Zenios (2000) investigates main performance drivers in ﬁnancial institutions and the roles of intermediations in that context. Bargaining theory provides a powerful tool for the analysis of intermediaries. As stated above, the intermediary must offer intermediated trade that is no worse than the outcome expected from direct negotiation. Bargaining theory helps to characterize expected outcome from direct negotiation in various situations. In the seminal work of Nash (1950), he deﬁnes the bargaining problem as “two individuals who have the opportunity to collaborate for mutual beneﬁts in more than one way. (p. 155).” There have been two main streams of research on bargaining theory: 1) axiomatic (cooperative game) models, and 2) strategic (non-cooperative game) models. Nash (1950 and 1953) lays the framework for the axiomatic Nash Bargaining Solution where he ﬁrst deﬁnes the basic axioms that any bargaining solution should “naturally” satisfy, he then shows that the solution of the so called Nash product uniquely satisﬁes the stated axioms. Kalai and Smorodinsky (1975) replace a controversial axiom from the original Nash proposal and revise the unique solution. Binmore (1987) summarizes the efforts over the years that either relaxes or adds to the Nash axioms and gives further analysis of the Nash’s bargaining model. An important characteristic of the axiomatic approach is that it leaves out the actual process of negotiations while focusing on the expected outcome based on prespeciﬁed solution properties. In this chapter, we will focus on non-corporative models of bargaining. St˚ hl (1972) is among the ﬁrst who investigates a nona cooperative, sequential bargaining process by explicitly modelling bargaining as a sequence of offers and counter offers. Using the notion of sequential bargaining, Rubinstein (1982) lays out the framework for non-cooperative bargaining models. He proposes an alternating-offer bargaining procedure where the agents take turns in making offers and counter offers to one another until an agreement is reached. The agents face time-discounted gain (a “shrinking pie”) which provide them the incentive to compromise. An intuitive comparison between the axiomatic and strategic bargaining theory can be found in Sutton, 1986. A majority of the earlier bargaining literature focuses on bilateral bargaining with complete information. There is a signiﬁcant and growing literature on sequential bargaining with incomplete information (c.f., Roth (1985), Wilson (1987)). In this setting, the players involve in the bargaining situation

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has only incomplete information about the opponent’s valuation. Rubinstein (1985a,b) proposes an alternating-offer model with incomplete information where player-one’s valuation is known but player-two’s cost takes one of two values, with a certain probability. He develops the concept of sequential equilibrium and shows that many sequential equilibria may exist, unless additional assumptions are made about the player’s beliefs. Myerson and Satterthwaite (1983) propose a mechanism design framework for bilateral bargaining where incomplete information is represented in the form of a distribution function with known supports. The mechanism design framework is more general than that of non-cooperative bargaining theory, and it provides a means to analyzing situations in multilateral settings. The latter has important implications in the context of supply chain intermediation, which we will also explore in this chapter. The rest of the chapter is organized as follows: in Section 2, we deﬁne the scope and set up the context for the theory of supply chain intermediation. In Section 3, we outline a modelling framework starting from bilateral bargaining with complete information, to bilateral bargaining with incomplete information, then multilateral bargaining with incomplete information. In Sections 4 to 6 we discuss each of these models in some detail. In Section 7 we conclude the chapter by pointing to related work in the supply chain literature and outlining future research opportunities.

2.

Supply Chain Intermediation

Many situations may arise in the supply chain where a group of suppliers and buyers ﬁnd beneﬁcial to seek the service of a third party agent as an intermediary. We may consider intermediaries in two broad categories: transactional intermediaries who improve the efﬁciency of a certain supply chain transactions (e.g., the wholesaler who facilitates the transactions between a group of manufacturers and retailers), and informational intermediaries who alleviate inefﬁciencies due to information asymmetry (e.g., an arbitrator, an auditor, an insurance agency). In either case, the intermediary must devise proper mechanisms (e.g., a long-term contract, a partnership agreement, auctions, etc.) to facilitate her operation. Supply chain intermediation refers to the coordination and arbitration functions provided by the intermediary. In the following, we summarize supply chain intermediation by the above categorization. Transactional Intermediary. Consider supply chain transactions from the customers, retailers, wholesaler/distributor, manufacturer, to the raw material suppliers. Each supply chain player can be viewed as a intermediary between her upstream suppliers and downstream customers. Over the long run, a supply chain player is only engaged when she creates

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value from such intermediation, she would be disengaged (disintermediated) otherwise. For instance, in a three-tier supply chain with retailers, wholesalers, and manufacturers, the wholesaler serves as an intermediary between the retailers and the manufacturers. Operationally, the wholesaler may create value by holding inventory for the manufacturers such that just-in-time delivery could be made to the retailers. Over time, the wholesaler may help reducing the manufacturer’s risk by aggregating demands from multiple retailers, or reducing the retailer’s shortage risk by offering alternative products from multiple manufacturers. Over the long-run, a certain manufacturers, wholesalers, and retailers may form strategic alliance to further improve efﬁciency by streamlining their transactions electronically, by joint forecasting and inventory planning, etc. While providing the service as an intermediary, the wholesaler incurs intermediation costs (i.e., overhead plus her own proﬁt) for the manufacturers and retailers. As market condition changes, the intermediation costs may not be justiﬁed by the reduction in transaction costs when comparing to direct exchange, or an alternative form of intermediation. In this case, disintermediation and/or reintermediation will eventually occur, i.e., a retailer may choose a new intermediary, say, a buy-side procurement auction for some of her products, while ordering directly from the manufacturer for other products. In general, a transactional intermediary may serve the following functions: reducing uncertainty by setting and stabilizing prices, reducing the costs associated with searching and matching, providing immediacy by holding inventory or reserving capacity, and aggregating supply or demand to achieve economy of scale. Informational Intermediary. While at the transactional level a supply chain may operate with a high level of transparency, at the tactical and strategic level it typically operates under incomplete or asymmetric information. Financial incentives represented by the buyer’s willingness-to-pay level and the supplier’s opportunity cost tend to be private information subject to distortion. The buyer and supplier may both have outside options that inﬂuence their bargaining positions, therefore their valuations. This information asymmetry could signiﬁcantly complicate the supplier-buyer interaction, leading to inefﬁciency known as adverse selection (i.e., players making misinformed decisions due to information distortion). This creates the needs for a third-party trust agent (an informational intermediary) who either acts as a broker between the trading parties, or as an arbitrator who regulates the trade in some way. In either case, the intermediary may devise mechanisms that elicit private information from the

The Internet channel operates most efﬁciently using drop shipping. thus the transaction overhead. Similar to a transactional intermediary.72
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players. and the preferred supplier program satisﬁes basic requirements of an efﬁcient mechanism. where a buyer may set up “preferred” status for a certain subset of suppliers. To successfully integrate the two channels. In this case. For instance. To the supply chain integrator. and synthesizing dispersed information to reduce information asymmetry. retailers in the traditional distribution channels must stock and own their inventory for shelf display. creating a trusted institution thereby reducing the needs for direct negotiation. an informational intermediary incurs her own costs and must create (net) value in order to justify her existence. In this context. the integrator may want to instigate different classes of service in the supply chain. and the supplier may have no way to verify the sourcing split the buyer actually uses (across all suppliers). thereby improving trade efﬁciency. suppose the leader of a vertically-integrated supply chain is to explore new strategies to integrate her Internet and traditional retail channels. A preferred supplier is given a guaranteed sourcing percentage (of a product) in exchange for better quality and favorite pricing. the new intermediary plays a critical role. However. If one is curious about the utilities of supply chain intermediary theory. The intermediary is to make sure that the buyer correctly ranks the suppliers based on her established criteria. Thus. On the other hand.
. In general. to stocking decision rights. the buyer may have no way to verify if the quality and pricing offered by a particular supplier is truly favorable (relative to other buyers). addressing issues ranging from demand management and inventory ownership. neither the supplier nor the buyer is willing to share information openly.” A supply chain integrator represents the leader of a vertically integrated supply chain. the integrator may create an informational intermediary to facilitate the preferred supplier program. who implements mechanisms that reconcile the conﬂicting goals and different operational requirements of the two channels. or a certain collective effort in the supply chain to improve overall efﬁciency. As another example. it may be helpful to consider the perspective of a supply chain “integrator. it may be necessary to replace the existing wholesaler with a new intermediary (reintermeidation). we may characterize informational intermediation as follows: avoiding adverse selection by administrating coordination mechanisms. where the wholesaler stocks and owns the inventory and ships products directly to the customers at the retailers’ request (see Chapter 14). the transactional and information intermediaries are strategic instruments who can be used to improve a certain aspect of supply chain efﬁciency.

buyers. and cardinality of interaction (bilateral vs. Under the multilateral setting. and (2) other competing forms of intermediary. The intermediary creates value by improving transaction efﬁciency and/or reducing the effects of information asymmetry. each buyer has a willingness to pay level v that could be public or private information depending on the model assumptions. we focus on the economic incentives of three types of players: suppliers. In the following section. The setting above describes the key elements we use to deﬁne supply chain intermediation. w). the intermediary optimizes her own proﬁt. and intermediaries. each supplier has an opportunity cost s. focusing on the roles of the intermediary in dividing system surplus and regulating trades. an intermediary must create intermediated trades that are more proﬁtable than (1) direct exchange between the suppliers and buyers. Supply Chain Intermediation Models: 1. Complete Information Bilateral Bargaining (Section 4) 2.Supply Chain Intermediation
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More generally. 3. multilateral). The intermediary offers an asked price w to the supplier and a bid price p to the buyer while creating a non-negative bid-ask spread (p − w) to support her operation. To be economically viable. All players are self interested. Incomplete Information Bilateral Bargaining (Section 5)
. To further characterize supply chain intermediation in different settings and scopes.
3. p. The intermediary has the authority to determine whether a particular trade is to take place using control β. while creating a system surplus that beneﬁt all players involved. Adopting some mechanism Γ(β. we establish the basic framework for supply chain intermediary theory. the supply chain integrator may consider strategically placing intermediaries in the supply chain to improve efﬁciency.1
Supply Chain Intermediary Theory The Basic Settings
To establish a framework for supply chain intermediary analysis. we further distinguish vertically integrated channels and matching markets. The value-creation is accomplished by overcoming obstacles that hamper proﬁtable trades and by preventing inefﬁcient trades from taking place. In the simplest form. proﬁt seeking. This characterization suggests the following simple taxonomy that we will use to structure the remainder of the chapter. incomplete information). and risk neutral. we consider models distinguished by two main factors: information symmetry (complete vs.

Roth (1985) and Wilson (1987) provide excellent surveys of this literature.2) As hinted above. but we do not consider this extension. the intermediary may choose to subsidize a short-term trade (violating condition (3)) for long-term proﬁt. This assumption provides a simple and unifying view between supply chain coordination and intermediation. For the incomplete information cases we need to make use of the mechanism design framework and the revelation principle. Consider the base model of bilateral bargaining under incomplete information. either serving as a mediator or an arbitrator. Thus.1) – Markets (Section 6. the intermediary has the option of calling off the trade. When any of the above conditions are not satisﬁed. all supply chain intermediation models discussed in this chapter assume a proﬁt-maximizing intermediary.. The intermediary. after providing necessary funds in support of the trade. (2) in the case of incomplete information. and to understand how could they extract proﬁt while sustaining the trade efﬁciency.g. In a more generalized case. This draws contrast to the existing supply chain coordination literature.
3. the intermediary must design an efﬁcient mechanism that offers the service. We will introduce an analytical model for each of cases listed above. The models help to characterize the role of intermediation. the result typically favors the leader of the channel who has the ﬁrst-move advantage. where the system surplus is divided among the players depending on the coordination mechanism (e.3 we will summarize the settings of the four supply chain intermediation models. the speciﬁc form of a contract). The proﬁtability of the intermediary symbolizes the strength of intermediated trade. the intermediary keeps the remaining system surplus. and (3) the player receives non-negative proﬁt. the intermediary must ensure that sufﬁcient system surplus is generated from the intermediated trade such that (1) the players are no worse off participating in the trade compared to their other options. A subset of the literature is concerned about
. always has an explicit interest in proﬁt. and the trade is ex post efﬁcient. to determine when should they exist. while the opposite signals the eventual fate of disintermediation. which we will brieﬂy summarize in the following section. the player has the incentive to reveal her true valuations. Simply stated. There is a signiﬁcant literature on strategic sequential bargaining models with incomplete information. We now introduce a mechanism design framework to characterize the main components of supply chain intermediation. In Section 3.2
Mechanism Design and the Revelation Principle
To carry out transactions at a lower cost.74
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Multilateral Trade (Section 6) – Vertical Integration (Section 6.

the players take their outside options. v) = 1). individually rational. The intermediary determines β(s. subject to incentive compatibility. In summary. and the intermediary determines if the trade is to take place. then the bargaining mechanism can be ex post efﬁcient. the buyer reveals her valuation v. It is individually rational if the players are no worse-off participating in the game than not participating. This mechanism design literature contributes two important concepts that are fundamental to bargaining analysis with incomplete information. Step 2. regardless of the actual mechanism being constructed. and individually rationality constraints. If the trade is not to take place (β(s. p. if a certain creiteria are satisﬁed = 0. the revelation principle Myerson. the intermediary collects asked price p from the buyer and pay the bid price w to the supplier. w) as follows: a. and ex post efﬁcient. To the intermediary. w) to maximize a certain well-fare function. The supplier reveals her valuation s. given the Bayesian-Nash equilibrium outcome of the mechanism we can construct an equivalent direct mechanism where the buyer and the supplier reveal their respective valuation to the intermediary.
. First. Based on the players’ reports. Otherwise. This allows the study of a large class of bargaining games without the need to specify each of the games in detail. the intermediary speciﬁes a mechanism Γ(β. A mechanism is incentive compatible if it is the best strategy for the players to reveal their true valuations. Second. If the trade is to take place (β(s. the players’ payoffs resulting from the bargaining process are Pareto efﬁcient. v) = 0). 1979 states that regardless of the actual mechanism constructed by the intermediary. v) which speciﬁes if the current trade is to take place: β(s. In other words. c. b. v) = 1. it is sufﬁcient to consider a direct mechanism as follows: Step 1. It can be shown that if there exists a bargaining mechanism where the corresponding bargaining game has a Bayesian-Nash Equilibrium that generates an ex post efﬁcient outcome. ex post efﬁciency requires that when all the information is revealed. The intermediary determines the bid-ask spread (p. it is sufﬁcient for the supply chain intermediary to consider a direct revelation mechanism that is incentive compatible.Supply Chain Intermediation
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the design of mechanisms that carry out the bargaining process. when putting into a mechanism design framework.

3
Models of Supply Chain Intermediation
We summarize four basic models for supply chain intermediation according to the taxonomy established earlier. 2. respectively. w) is ex post efﬁcient while balancing the budget (otherwise. the intermediary ensures that mechanism Γ(β. The intermediary determines (β. The intermediary determines β. The above procedure offers a general mechanism design framework for supply chain intermediation.
3. If so. she collects asked price p from the buyer and pay bid price w to the supplier. v)). the supplier and the buyer hold private information s ∈ [s1 . Each bidder i reports her valuation vi to the intermediary. collect the amount pi (s. Given s and the vector of the reported valuations v = (v1 . the intermediary is to call off the trade).1-(c)) there is one supplier and m buyers (bidders). and ex post efﬁciency (see Section 5). bi ] which is known to the others in the form of distribution function Gi : [ai . If so. Figure 3. v) to the supplier. 1. In multilateral trade with vertical integration (Figure 3. 1]. Each bidder i holds private information about her valuation vi ∈ [ai .1). v2 ] as deﬁned above with ex ante distributions F (s) and G(v).1-(b)). w to maximize a certain function subject to incentive compatibility.e. p. In the following section. vm ). bi ] → [0.1-(a)). 3. the intermediary determines the probability βi (s. v) from each bidder i.. . the supplier reports her opportunity cost s. This is followed by three incomplete information cases. The intermediary determines if the trade is to take place (β) based on the cost information. v ∈ [v1 . The intermediary decides if the trade is to take place (β(s. p. she collects p(s..
. w to maximize a certain function subject to individual rationality (see Section 4).. In bilateral bargaining with incomplete information (Figure 3. The intermediary determines β. v) that bidder i will get the object (i. v) to the supplier. p. determines which bidder gets the object).1 illustrates the schematics for the four different models of supply chain intermediation. and pay w(s.. In bilateral bargaining with complete information (Figure 3. w) to maximize a certain function subject to incentive compatibility and individual rationality (see Section 6. individual rationality. The simplest model is the complete information case based on bilateral bargaining with complete information. we use this framework to consider a few different settings. s2 ].76
Handbook of Quantitative Supply Chain Analysis
In general. v) from the buyer and pay w(s. the supplier’s opportunity cost is s and the buyer’s willingness to pay is v. p.

In multilateral trade with markets (Figure 3.b2]. and each supplier’s cost is distributed according to F (s).vm)
Buyer(1)
v(1) ≥ v(2) ≥ … v(m) G(v) v=(v1.n)
Buyer(2)
…
Buyer(m)
(d)
Figure 3.v)
Intermediary
p(s. β m
pm(s.v)
Buyer
s
v
s∈ [s1.
4. G(v)
(a)
w (s.vm)
Intermediary
…
Supplier(n)
p0 k=min (m. G2(v2)
s
β 1 .….
Models of Supply Chain Intermediation
4. It is the common believe of all traders that each buyer’s value is distributed according to G(v). The supplier produces (or acquires) the product at a unit cost of s.…. Suppose there are positive net gains π d
. The buyers and the suppliers report their valuations to the intermediary.2). There is one supplier who is to provide a certain product to a buyer. n) and determines the market clearing price p0 subject to budget balanceness (see Section 6.s2].bm].b1].Supply Chain Intermediation
w
Intermediary
77
p w (s.1.v)
…
Buyerm
vm∈ [am.v)
Supplier Intermediary
(b)
p1(s. The buyer is willing to pay v for each unit of the good. G1(v1) v2∈ [a2.sn) s(2) ≤ … s(n)
Supplier(1) Supplier(2)
v=(v1. each buyer i has a private valuation vi for a single unit of good. F(s)
v∈ [v1.v)
Buyer1 Buyer2
v1∈ [a1. Gm(vm)
(c)
s(1)≤ F(s) s=(s1.….1-(d)) there are m buyers and n suppliers.v)
β
Supplier Buyer Supplier
β (s.
Bilateral Bargaining with Complete Information
We now present a simple supply chain intermediary model based on the setting of bilateral bargaining with complete information.v2]. The supplier and the buyer may choose to trade directly. who ﬁnds the efﬁcient trade quantity k ≤ min(m. in which case a transaction cost T incurs. and each supplier j has a privately known cost sj for the good she sells.….

the supplier and buyer may choose to trade directly. The intermediary posts the bid-asked prices based on a certain criteria. such that the buyer receives α · π d and the supplier receives (1 − α) · π d . The intermediary makes a binding offer of an asked price p and a bid price w. i. Otherwise.2. Based on the posted price. or intermediated trade based on the unit price. the buyer and the supplier decide whether to trade directly with one another.2) and (3. if v ≥ p and w ≥ s = 0. while incurring a transaction cost T . Step 2. while incurring a transaction cost of K.78
from the trade. or through the intermediary.
(3. This simple model captures the basic decisions faced by the supplier and the buyer: to use direct. where the intermediary determines if the trade is to take place based on the following criteria: β(s. If the supplier and buyer are to transact via the intermediary. Clearly the intermediated trade will occur if and only if it offers a lower transaction cost.3)
The intermediary sets the bid-ask spread (p − w). then:
Handbook of Quantitative Supply Chain Analysis
π d = v − s − T > 0.1)
Suppose that an intermediary can purchase the goods from the supplier at unit price w and sell it to the buyer at unit price p. the sequence of events is as follows: Step 1. The above posted price model can be described in the form of a direct mechanism as speciﬁed in Section 3. In the former case.2) (3. If they trade directly. they must bargain over the allocation of the gain π d . she must offer an asked price p and a bid price w such that v − p = α · πd w − s = (1 − α) · π d (3. the supplier and the buyer must split the net gain through bilateral bargaining. After observing p and w. trade takes place at p and w with a transaction cost of K. or to accept the intermediary’s offer. For a typical trade.4)
. K ≤ T . v) = 1.. which is equal to the transaction cost T according to (3.3): (p − w) = (v − α · π d ) − ((1 − α) · π d − s) = v − s − π d = T (3. In order for the intermediary to attract the supplier and the buyer to the intermediated trade.e. 1]. Step 3. Suppose the bargaining results in a split α ∈ [0.

. the retailer accepts or rejects the contract. In this context.. Rubinstein (1982) lays out an alternating offer bargaining procedure where the agents face time-discounted gain. Cachon (2002) describes the typical sequence of events as follows: “the supplier offers the retailer a contract.Supply Chain Intermediation
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The intermediary’s proﬁt is generated from the bid-ask spread after taking out the transaction cost. the intermediary can only extract proﬁt if she could offer a more efﬁcient transaction with K < T . Ponsati and Sakovics (1998) also consider outside options as part of the Rubinstein model. Binmore et. q. or improve the terms of trade relative to direct exchange.e. 1990) use models of bargaining and searching to present markets as decentralized mechanisms with pairwise interactions of buyers and suppliers. assuming the retailer accepts the contract. there is no time pressure (time-discounted gain). and in each iteration. i. Binmore and Herrero (1988) propose a third option where an agent may decide to leave the current negotiation and opt for her “outside options” (e.f. Muthoo (1995) considers outside options in the form of a search in a bargaining search game. and how the players’ bargaining power inﬂuence the surplus division.. Economists (c. while at the same time achieving the expected beneﬁt brought by direct bargaining..
4. the retailer submits an order quantity. or (2) propose a counter offer. 1985.1
Bilateral Bargaining to Divide the System Surplus
One important function for the intermediary is to provide a shortcut to the otherwise lengthy. we present a supply chain bargaining model which further characterizes how the system surplus (the gain of trade π d ) is divided. Thus. intermediaries could either increase the likelihood of matching. The most well known model of pairwise supplier-buyer interaction is in supply chain contracting. al (1986) study a version of the alternating offer model with breakdown probability. The supply chain literature takes a different perspective on supplier-buyer interaction. meaning that the negotiation breaks down. An important aspect of the extended bargaining model is to allow the possibility for the negotiation to breakdown. (p − w − K) = T − K.g. an agent must decide to either (1) accept the opponent’s offer (in which case the bargaining ends). previously quoted deals). Bilateral bargaining provides the basis for an intermediary to design an efﬁcient trade and to determine a bid-ask spread that is sufﬁciently attractive from the players’ perspectives. Rubinstein and Wolinsky. In the following section. In this model. and possibly costly negotiations between the supplier and the buyer. The scope of the contract is typically limited to the two agents involved in the negotiation at a particular point in time with the assumption that they have agreed to coordinate via some form of contract. but there is a probability that a rejected offer is the last offer made in the game.

and (2) rather than settling for a predetermined split of the channel surplus. The above approach encounters two basic problems when considered in the broader context of supply chain coordination: (1) there is no guarantee that either agent involved in the current negotiation should necessarily accept the “channel coordinated” contract when other outside options are easily accessible. both players may desire to negotiate for a (hopefully) larger share of the surplus.. second. The bargaining model offers an alternative view of supply chain interaction as follows: ﬁrst. the viewpoints offered by supply chain intermediary theory and bargaining theory broaden the scope for supply chain coordination and allow for additional versatility in modelling. In the following section. season demand occurs. typically in favor of the “leader” who initiates the contract design. instead of assuming the contract terms would be accepted in one offer. and the equilibrium condition for the bargaining game may not coincide with contract stipulation. we model the pair-wise supply chain interaction as a bilateral bargaining game with complete information. If the retailer rejects the contract.” A typical goal for supply chain contracting is to design “channel coordinated” contracts (i. and ﬁnally transfer payments are made between the ﬁrms based upon the agreed contract. determines the ultimate split of the channel surplus. We will summarize main results derived in Ertogral and Wu (2001). alternating-offer bargaining game on the contract surplus. Ertogral and Wu (2001) show that the dynamics of supplierbuyer contract negotiation would change fundamentally if the agents were to enter a repeated. The channel surplus created by the coordination contract is split arbitrarily.80
Handbook of Quantitative Supply Chain Analysis
to the supplier.
. while at the same time satisﬁes individual rationality and incentive compatibility constraints. the game ends and each ﬁrm earns a default payoff. the agents are thought to be justiﬁed to accept the contract terms. third. As we will argue throughout this chapter.e. the players’ corresponding bargaining power. an alternating-offer bargaining process takes place before a ﬁnal agreement is reached. and introduce a bargaining theoretic perspective which help to analyze the tradeoff between direct and intermediated exchanges. So long as that is the case. the supplier produces and delivers to the retailer before the selling season. Outside options play a role here. shaping the agent’s perception of her bargaining power. contract negotiation is generalized to a bilateral bargaining over the expected channel surplus. not the pre-determined contract stipulation. contracts where the players’ Nash equilibrium coincides with the supply chain optimum).

and other intangibles that can not be measured by monetary gains (e. The outside option is important as a player’s
. We assume that the total maximum surplus generated from the current trade is greater than or equal to the sum of the outside options.g. and (3) each player has an outside option. which she could fall back on. The sequence of events in the bargaining game is as follows: 1 With equal probability. say π = π d . which could be inﬂuenced by either player’s anticipation of a more attractive future deal.. The breakdown probability is deﬁned exogenously here but could perceivably be modelled endogenously with some added complexity. and would have no incentive to participate in the ﬁrst place. e. 4 If the negotiation continues.offer bargaining model with three additional elements: (1) both players are equally likely to make the next offer. The ﬁrst treatment allows us to view each iteration of the bargaining processes independently regardless of who makes the previous offer. 3 With a certain probability. Before entering negotiation. We further assume that when an agent is indifferent between accepting the current offer or waiting for future offers. The breakdown probability characterizes the stability of the bargaining situations. negotiations a player previously carried out with other agents in the market. trust and goodwill. either the supplier or the buyer makes an offer that yields a certain split of the system surplus π 2 The other agent either accepts the offer (the negotiation ends).2
A Bilateral Supply-Chain Bargaining Model
Consider a bargaining situation between a pair of suppliers and buyers who set out to negotiate the terms associated with a certain system surplus. (2) the negotiation breaks down with a certain probability. The supplier and the buyer are to make several offers and counter offers before settling on a ﬁnal agreement. non-perfectly rational players. (1 − ψ). This is reasonable since otherwise at least one of the players will receive a deal worse than her outside option. the supplier and buyer each have recallable outside options Ws and Wb . the game restarts from step 1.g. The above bargaining game is similar to Rubinstein’s alternating. the negotiation breaks down and the agents take their outside options.Supply Chain Intermediation
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4. Intangibles such as an anticipated future deal is not considered an outside option. she will choose to accept the current offer. respectively. We limit the deﬁnition of outside options to tangibles known at the point of negotiation.. rejects the offer and waits for the next round offer. Ws and Wb . or there lack of).

Thus. the subtree repeats same structure. mb (ms ) : The minimum share the buyer (the supplier) could receive in a subgame perfect equilibrium for any subgame initiated with the buyer’s (the supplier’s) offer.
4. with probability (1 − ψ) the bargaining breaks down. an agent would accept a proposal if it offered at least as much as what she expected to gain in the future. In a perfect equilibrium. The player with higher valuation on her outside option is more likely to receive a larger share of the surplus. and ms to Ms for the supplier. where the buyer and the supplier have equal probability (ψ/2) to make the next offer. where
. or when the negotiation breaks down (Step 3). We then show that the player’s share under each of the four extreme cases mb . ψ : The probability that negotiations will continue to the next round. We will analyze the game in a time line of offers to ﬁnd the subgame perfect equilibrium. Given the derived shares. If the buyer makes the next offer. With probability ψ the bargaining continues to the next round. similar to the approach taken in Shaked and Sutton (1984) and Sutton (1986). each subgame starts with the same structure: either it is initiated by the supplier or the buyer. We introduce the following additional notations: Mb (Ms ) : The maximum share the buyer (the supplier) could receive in a subgame perfect equilibrium for any subgame initiated with the buyer’s (the supplier’s) offer. This best-case scenario is illustrated in Figure 3. Mb .2.3
The Subgame Perfect Equilibrium
The bargaining game outlined above iterates until one of the agents accepts the offer (Step 2).1. The subgame perfect equilibrium (SPE) strategies are the ones that constitute the Nash equilibrium in every iteration of the game (the subgame). If the supplier makes the next offer. The root node represents that the buyer makes the initial offer. given the strategy set of the other agent. The subgame equilibrium analysis proceeds as follows: we ﬁrst assume that in subgame perfect equilibrium there is an inﬁnite number of solutions leading to gains ranging from mb to Mb for the buyer. we can then determine if there is a unique SPE solution for the players where mb = Mb and ms = Ms . with probability (1 − ψ) the bargaining breaks down. In this bargaining game. ms and Ms can be derived from an event-tree structure shown in Figure 3. We now derive the best-case scenario for the buyer where she initiates the subgame and receives the maximum possible share Mb in SPE. the perfect equilibrium strategies of the agents are symmetrical in each subgame. again.82
Handbook of Quantitative Supply Chain Analysis
bargaining power is a combination of her ability to inﬂuence the breakdown probability and her outside options. With probability ψ the bargaining continues to the next round.

When the buyer makes the offer. the buyer’s maximum gain would be labelled in terms of the supplier’s share π − Mb .2 represents the share the supplier would receive in perfect equilibrium. she settles for the minimum perfect equilibrium share ms . when the supplier makes the offer. For convenience. the nodal label in Figure 3. If the supplier makes the offer.2. In case the bargaining breaks down. The subtree from this point on repeats the same structure. the supplier receives her outside option Ws . When the buyer makes the offer. while the supplier’s minimum gain is labelled ms . she settles for the least amount she expects to gain in the future. she receives the maximum gain possible and leaves π − Mb to the supplier.Supply Chain Intermediation
Supplier
83
ψ
2
ms
Supplier
ψ
2
Buyer
ψ
2
[(1 −ψ )Ws +
ψ
2
(π − M b + ms )]
(π − M b )
ψ
2
1 −ψ
Buyer Breakdown
Buyer
ψ
2
ψ
[(1 −ψ )Ws + (π − M b + ms ) 2 2 + π − M b ] + (1 −ψ )Ws
ψ
1 −ψ
ψ
2
(π − M b )
Ws
Breakdown
Ws
Figure 3. equilibrium
A tree deﬁning the largest share the buyer could obtain in a subgame perfect
the buyer and the supplier have equal probability (ψ/2) to make the next offer. Since the event tree in the ﬁgure represents the case where the buyer gets the largest possible perfect equilibrium share. Thus. To derive the SPE condition we evaluate the event tree backward from the leaf nodes.5)
. she leaves π −Mb to supplier as before. The offers at the next tier follows the same logic. which is equal to ψ (π − Mb + ms ) 2
(1 − ψ)Ws +
(3.

she ask for the difference between the system surplus π and the supplier’s (buyer’s) outside option Ws ψ2 (Wb ) minus a “risk premium” equals to − 2(2−ψ) (π − Wb − Ws ). If they do not reach an agreement and continue with the bargaining.9) and (3. we may conclude that Mb = mb = Xb and Ms = ms = Xs . One important issue remains is whether there exists a ﬁrst-mover advantage in the game. In the following.4
Analysis of the Bargaining Game
Under complete information. The advantage diminishes as the probability of breakdown decreases.11) 2−ψ
Since 2 ≥ ψ 2 + ψ and (π − Wb − Ws ) ≥ 0.10)
Proof: By solving the system of equations given in Proposition 1. and the opponent would accept the offer. where Xb = (π − Ws ) − Xs ψ2 (π − Wb − Ws ) 2(2 − ψ) ψ2 = (π − Wb ) − (π − Wb − Ws ) 2(2 − ψ) (3.9) (3. we may conclude from Proposition 2 that the bargaining process will end in one iteration when either the supplier or the buyer initiates the negotiation with the SPE offer.Supply Chain Intermediation
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for Xb (Xs ) share of the system surplus π. that the players could share if they reach an agreement. the SPE strategy is unique.
4.
Proposition 3 The ﬁrst-mover advantage exists in the alternating offer bargaining game. We attend to this issue in the following proposition. there is a risk that the process will break down and they receive only their respective outside options (thus the mutual gain would be lost). or equivalently when the breakdown probability (1 − ψ) is zero. It is zero when ψ = 1. Note that the risk premium is a fraction of the “mutual gain” (π −Wb −Ws ). This is true since the SPE offer makes the opponent indifferent between accepting the current offer and waiting for future offers. We may interpret from expressions (3.10) that when a buyer (supplier) makes an offer. and goes to zero if the probability of breakdown is zero. the above expression always yields a value greater than or equal to zero. Since the maximum and the minimum SPE shares are equal for a given player. we
.
Proof: If we take the difference between the SPE shares of the two players we get the following: Xb − (π − Xs ) = Xs − (π − Xb ) = (π − Wb − Ws )(2 − ψ 2 − ψ) (3. Proposition 2 says that in equilibrium the initiating party would offer a fraction of the mutual gain to the opponent that is sufﬁcient to neutralize the opponent’s desire to continue with the bargaining process.

13)
This expression is always positive as well. and linearly decreasing in her opponent’s outside option. and the player who accepts the SPE offer both gain no less than their respective outside options.12)
The expression above is always positive. Therefore. 2(2 − ψ)
= 0. Another interesting aspect of the bargaining game is that. Hence the player who initiates the SPE offer will gain no less than her outside option.
Proposition 4 The player who initiates. the offering party obtains the maximum share when the breakdown probability approaches 1 as described in the following proposition. In the following. the difference between her SPE share and her outside option is as follows: X b − Wb = X s − Ws = 1 (π − Wb − Ws )(4 − ψ 2 − 2ψ ) 2 2−ψ (3. = −(4 − ψ 2 − 2ψ) < 0. regardless of who initiate the offer.
Proof: Taking the ﬁrst and second derivatives of the buyer’s SPE offer with respect to the outside options Wb and Ws . we see that ∂Xb ∂Wb ∂ 2 Xb ∂Wb2 ∂Xb ∂Ws ∂ 2 Xb 2 ∂Ws = ψ2 ≥ 0. we further specify the relationship between the breakdown probability (1 − ψ) and the SPE share of the initiating player.86
Handbook of Quantitative Supply Chain Analysis
show that the players’ individual rationally conditions are satisﬁed under SPE.
It should be clear that the case when the supplier initiates the SPE offer would lead to similar results. in SPE both players gain no less than their outside options. For the player who accepts the SPE offer.
.
Proposition 5 The SPE share of the initiating player is linearly increasing (for ψ > 0) in her outside option. 2(2 − ψ)
= 0.
Proof: For the player who initiates the offer. the difference between her SPE share and her outside option is as follows: (π − Xs ) − Wb = (π − Xb ) − Ws = 1 (π − Wb − Ws )ψ 2 2 2−ψ (3.

we will now examine the role of supply chain intermediary in setting prices. Recall that a supply chain intermediary is economically viable if she can carry out transactions at a lower cost than (1) direct exchange between the suppliers and buyers.15)
Proof: From Proposition 2 we know that the supplier and the buyer would expect from direct bargaining a payoff no less than (π − Xb )and π − Xs . Thus. taking the ﬁrst derivative of the buyer’s SPE offer with respect to ψ gives: ∂Xb 1 ψ[(ψ − 4)(π − Wb − Ws )] = ∂ψ 2 (2 − ψ)2 (3.
Proof: Suppose the buyer is the offering player. there is no reason for the offering player to offer more than the opponent’s outside option.14)
Since ∂Xb ≤ 0 for 0 ≤ ψ ≤ 1. If we use the result of bilateral bargaining to represent the expected gain the supplier and the buyer would expected from direct exchange. It should be clear that the case when the supplier initiates the SPE offer would lead to similar results. and (2) other competing intermediaries.5
Intermediary’s Role in Price Setting. respectively.” and “reducing the costs associated with searching and matching.” We ﬁrst establish the pricing criteria for a supply chain intermediary. Using the categorization in Section 2.Supply Chain Intermediation
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Proposition 6 The SPE share of the initiating player is maximized when the breakdown probability approaches 1 ((1−ψ) → 1). these are transactional intermediation aiming to “reducing uncertainty by setting and stabilizing prices.
4. the player initiating the bargaining would know that her opponent (in anticipation of the breakdown) is willing to accept an offer equivalent to the outside option. To attract the supplier and the buyer from direct bargaining. ∂ψ we may conclude that Xb is maximized at ψ = 0. where the share equals to the system surplus π less the opponent’s outside option. Proposition 6 is intuitive in that if both players know that the negotiation is likely to breakdown ((1 − ψ) → 1).
Theorem 1 A supply chain intermediary is viable if she can operate with a transaction cost no more than
(v − s) − Wb − Ws − ψ2 (π − Wb − Ws ) (2 − ψ) (3. and we have assumed that π − Wb − Ws ≥ 0. we may establish the role of any supply chain intermediary between the buyer and the supplier as follows. a supply
. and Matching
Given the bilateral supply chain bargaining model and the supply chain intermediary theory described above. and in matching suppliers with buyers. Searching.

she may offer a transaction cost up to (v − s − Wb − Ws ). the higher the breakdown probability the easier it is for the intermediary to stay viable. the intermediary must offer a transaction cost no more than (v − s − π). The above analysis provides the following insights concerning supply chain intermediation:
When both the supplier and the buyer are in weak bargaining positions (limited outside options).
Note that the above insights are derived entirely from marginal cost analysis under complete information. etc.Supply Chain Intermediation
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occur.
5. Moreover. This analysis is based entirely on marginal costs. respectively. the breakdown probability (1 − ψ) plays a role. when either the supplier or the buyer is in a strong bargaining position. intermediated trade will be desirable. In Sections 3 and 4 we combine the theoretic foundation established by Spulber (1999) and Rubinstein (1982) to deﬁne a posted-price model of the supply chain intermediary theory. Speciﬁcally. disintermediation is likely to occur. and the trade takes place if and only if the buyer and the supplier agree to the ask and bid prices. This is the subject of discussion in the remainder of the chapter. If the interaction is direct. Conversely. the bargaining-theoretic outcomes provide the rationale for the third-party intermediary to perform her intermediation functions. breakdown probability. Speciﬁcally. it can be modelled explicitly as a bargaining process. the intermediary must offer prices such that the players are no worse off than bargaining directly with one another. or when direct trade is expected to be stable. To establish the bid-ask spread. the intermediary is to carry out the expected bargaining outcome via an efﬁcient mechanism. Rather. In general. the intermediary posts the bid-ask spread. when the breakdown probability is zero (ψ = 1). In this model. When the breakdown probability is 1 (ψ = 0). or when direct trade is expected to be volatile (as characterized by the breakdown probability).
Bilateral Bargaining with Incomplete Information
The supply chain intermediary theory takes the viewpoint that supplierbuyer interaction could be either direct or intermediated. The Rubinstein (1982) model allows us to consider a richer set of bargaining parameters such as bargaining power. Thus. If it is intermediated. while eliminating the needs for bilateral bargaining to actually take place. the bargaining theoretic analysis does not suggest that every supplier-buyer negotiation is actually taking place as a bilateral bargaining game. and no consideration are given concerning information asymmetry. which is sufﬁcient if we assume the play-
. the intermediary must convince the players that they are not worse off than they would be with direct bargaining.

each player may hold private information on her valuation of the object. He shows that many sequential equilibria may exist.90
Handbook of Quantitative Supply Chain Analysis
ers and the intermediary have complete information. We demonstrate that the bargaining power of supply chain participants determines the nature of their interactions. 1985b introduces the alternating-offer model with incomplete information. the buyer holds private information on her willingness to pay level v . they also serve as signals by which the players communicate their private information. In this section. the supply chain intermediary establishes intermediated trade via a mechanism. We introduce the analytic framework established by Myerson (1982). taking on the interval [v1 .e. 1985a. i. we are interested in the case where the supplier holds private information on her opportunity cost s. The supplier holds private information on her opportunity cost s. the offer and counter offers not only express a player’s willingness to settle on the deal. The players hold private information on their costs. Speciﬁcally. her outside options. We then introduce potential research topics using this perspective.v2 ]. For the alternating-offer bargaining game described above. with cumulative distribution G. Rubinstein (1985a. Such signals may not be truthful as both parties may have incentive to distort the signal if doing so could increase their gains. To further reﬁne the notion of sequential equilibrium in bargaining. There is a signiﬁcant and growing literature on bargaining with incomplete information.. which takes values on the interval [s1 .
5. and den˜
. We show that players’ relative bargaining power could be used to characterize when an intermediated trade is viable and when disintermediation is likely. and the buyer holds private information on her willingness to pay level v.b)Rubinstein. and cumulative distribution function F (s). or her quality level/expectation. Rubinstein. one-supplier basic model where the players could either trade through an intermediary. and Myerson and Satterthwaite (1983) that lays out the foundation for intermediated trades under incomplete information. established based on their respective outside options. Acting on this information. Similarly. we consider the case when players are subject to asymmetric information.s2 ] with ˜ a prior probability density function f (s). and he deﬁnes unique equilibrium outcomes by adding conjectures on the way players rationalize their opponents’ bargaining power.1
The Basic Setting
We consider a one-buyer. which directly inﬂuence the bargaining process. or via a direct matching market (their outside option). Earlier literature in this area uses the notion of a sequential equilibrium due to Kreps and Wilson (1982) by reducing the bargaining situation to Harsanyi’s (1967) game with imperfect information.

By the revelation principle (Section 3. Each player knows her own valuation at the time of trade. If so. p(s. respectively. w) represents the direct revelation mechanism. v) is the expected payment to be made by the buyer to the intermediary (the asked price). the intermediary has two main advantages: (1) she has access to aggregate information gained by dealing with multiple buyers and suppliers over time. but considers the other’s valuation a random variable. Let Γ(β.17) Ψb (v) = v − g(v) Similarly. respectively. where s and v are the valuations given by the supplier and buyer. and ex post Pareto efﬁciency at the same time. where β(s. given the equilibrium of the mechanism. In competition with the players’ outside options. the intermediary is aware of the buyer and the supplier’s outside options as random variables characterized by distributions G and F. or calls off individual transactions. and w(s. the intermediary must offer an intermediated trade that is “more attractive” to the buyer and the supplier. a proﬁt maximizing intermediary could tax the market by setting a bid-ask spread. subsidizes. however. Otherwise. rejecting an unproﬁtable trade. we can construct an equivalent incentive compatible direct mechanism. regardless of the mechanism constructed by the intermediary. where the buyer and the supplier report their respective valuations to the intermediary. Based on this information the intermediary establishes the buyer’s virtual willingness to pay Ψb (v) as follows: 1 − G(v) (3. which states that it is impossible to design a mechanism that satisﬁes incentive compatibility. p.18) Ψs (s) = s + f (s)
. In other words. and (2) she has the freedom to design an intermediated trading mechanism that taxes. and the intermediary determines if the trade is to take place. The intermediary is subject to the same information asymmetry in the market as the market participants. v) is the probability that the trade will take place. it is sufﬁcient to consider an incentive compatible direct mechanism.Supply Chain Intermediation
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sity g. the players take their outside options in a direct matching market. Since the intermediary does not need to balance the budget in every single transaction as is required in a direct matching market. distributed as above. As mentioned above.2). the intermediary establishes the supplier’s virtual opportunity cost Ψs (s) as follows: F (s) (3. budget balanceness. she determines the buyer’s payment and the suppliers’ revenue. For instance. or subsidizing the trade while achieving budget balance (and proﬁt) over the long run. v) is the expected payment from the intermediary to the supplier (the bid price). The latter is important due to the impossibility theory by Vickrey (1961). Myerson and Satterthwaite (1983) show that it is possible to design an incentive compatible mechanism that is ex post efﬁcient.

v) = 0). Based on the players’ reports. v) =
v1
(p(τs .29) subject to incentive compatibility. the buyer reveals her valuation. v) = 1). the total expected gains from
. v) = 1. her outside options. if Θ(Ψb (v). characterized by s. 4 The intermediary must ensure that mechanism Γ(β. The intermediary speciﬁes a mechanism Γ(β. v) which speciﬁes if the current trade is to take place: β(s. The expected gain of trade from the buyer’s (supplier’s) perspectives is πb (πs ) as deﬁned in (3. τb ) − w(τs . w) is ex post efﬁcient.Supply Chain Intermediation
93
nism that is individually rational. w) as follows: 1 The intermediary determines β(s. and the probability distributions G and F characterizing the asymmetric information. and her quality requirements. y) speciﬁes the relationship between x and y. 2 If the trade is to take place (β(s. the players take their outside options. We know that any Bayesian-Nash equilibrium of any trading game with intermediary can be simulated by an equivalent incentive compatible direct mechanism. her outside options. and individually rationality constraints. and ex post efﬁcient. The supplier reveals her valuation. τb ))f (τs )g(τb )dτs dτb
(3. in reference to the trade at hand. where Θ(x. To the intermediary. the intermediary constructs a virtual willingness to pay ψb (v) for the buyer a virtual opportunity cost ψs (s) for the supplier. Otherwise. 3 If the trade is not to take place (β(s. The intermediary is subject to the same information asymmetry as the players. characterized by v. Step 2.23) ((3. the intermediary speciﬁes a bid-ask spread (p. Ψs (s)) is satisﬁed = 0. incentive compatible. p. Step 3. and her quality type.24)). We further illustrate the construct of this framework in the remainder of this section. w) to maximize her own expected proﬁt
v2 s2 s1
πI (s. Thus. p. Following the supply chain intermediary framework we may specify intermediation under bilateral bargaining with incomplete information as follows: Step 1.

We describe the construct of such a mechanism in the following. With Theorem 2. τb )dτs dτb
−
Rewriting the above relationship using the deﬁnition of Ψb (.17) and (3.35) Based on the supply chain intermediation framework outlined above. πI + πb (v1 ) + πs (s2 ) = −
s s2 v1
(1 − G(τ ))F (τ )dτ
(3. Otherwise. v) = 1. w) to maximize her proﬁt (3. (3. v) which speciﬁes whether the trade is to take place given the reported s. p. otherwise the trade is not taking place. The latter could be done by a mechanism which only allow proﬁtable (while individually rational) trades to take place. τb ))f (τs )g(τb )dτs dτb −πb (v1 )−πs (s2 )
(3. Myerson and Satterthwaite (1983) shows that it is possible to construct an ex post efﬁcient mechanism so long as the trade is subsidized by an intermediary as needed. we may rewrite the intermediary’s proﬁt function as follows:
v2 s2 s1
πI =
v1
(Ψb (τb )−Ψs (τs ))β(τs . we have the following relationship: πI + πb (v1 ) + πs (s2 )
v2 s2 s1 v2 v1 s2 s1
=
v1
(τb − τs )β(τs . v12 (1 − G(τ ))F (τ )dτ is the minimum subsidy required from the intermediary.35) it is straightforward to ﬁnd a proﬁt maximizing β subject to individual rationality as follows: β(s. or design a trading mechanism that would maximize her proﬁt in each individual trade. A mechanism is ex post efﬁcient iff the buyer gets the object whenever her valuation v is higher than the supplier’s cost s. However.18) gives us the equation stated in the theorem. First. The former requires enhanced knowledge of the market which presents an interesting research topic to be discussed further.Supply Chain Intermediation
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Thus.) and Ψs (.34)
Thus. Speciﬁcally. the intermediary devises a direct mechanism Γ(β. v and her knowledge of their virtual opportunity costs and virtual willingness to pay.35). the intermediary must determine β(s.) in (3.36)
. Using Theorem 2. Given the simple form of the proﬁt function (3. if Ψb (v) ≥ Ψs (s) = 0. a proﬁt-minded intermediary may want to optimize her proﬁt over a longer time horizon. subject to incentive compatibility and individual rationality. τb )f (τs )g(τb )dτs dτb (F (τs )g(τb ) + (1 − G(τb ))f (τs ))β(τs .

the intermediary must specify an asked price p(s. to maximize her own proﬁt the intermediary must restrict the trade to “proﬁtable” situations.. v) that satisfy the incentive compatibility constraints (3.25) and (3.
In essence. An important extension for this line of 2 research is to model the situation where the intermediary subsidizes a certain unproﬁtable trades with the goal of maximizing gains over a longer horizon. this results in a fairly conservative policy for intermediated trade. e. Then among all individually rational mechanisms. 2 The insights provided by the above analysis is important in that it illustrates another important role played by the supply chain intermediary. Of course. the intermediary’s expected proﬁt is maximized by a mechanism in v s which the trade takes place iff Ψb (˜) ≥ Ψs (˜). In theory.36) the intermediary’s proﬁt (based on (3. Then. one way for the intermediary to manage is by regulating when the trade is to take place. In other words. suppose s and v are both uniformly distributed on the unit inter˜ ˜ val. In other words. while paying the supplier the highest possible opportunity cost.) are monotone functions. the intermediary asks the lowest willingness to pay level the buyer could have quoted. Or equivalently. Note that under the criteria speciﬁed in (3. Ψb (v) ≥ Ψs (s)).e. it can be shown that if Ψb (. one possible solution is to set p(s. However.
Theorem 3 Suppose Ψb (. In other words. v2 ] and [s1 .. Under this mechanism the intermediary’s proﬁt is determined by the difference between the buyer’s virtual willingness to pay and the supplier’s virtual opportunity cost. the intermediary must subsidize trade as needed. in order for the trade to occur in the ﬁrst place. Ψs (s)) ≡ Ψb (v) ≥ Ψs (s). v) = v1 and w(s. From Theorem 2. Moreover.35)) is always non-negative.) and Ψs (.g. v) and a bid price w(s. while never sponsoring any trade that she is expected to subsidize. the trade 2 takes place iff the buyer’s valuation exceeds the supplier’s valuation by 1 .. We now state the following theorem (Myerson and Satterthwaite (1983)).) and Ψs (. s2 ]. while the intermediary satisﬁes the individual rationality constraint she offers no additional surplus to the players. the buyer’s valuation must exceed the supplier’s by 1 . v) = s2 . but it is possible for the intermediary to regulate trades based on the players’ virtual valuations such that only trades expected to be proﬁtable are actually taking place. based on the above mechanism the trade takes place if and only if v v s s ˜ ˜ Ψb (˜) = 2˜ − 1 ≥ 2˜ = Ψs (˜). i. it must be the case that Ψb (v1 ) ≥ Ψs (s2 ). as indicated by the difference between the buyer’s virtual willingness to pay and the supplier’s virtual opportunity cost. respectively. v − s ≥ 1 .e.26). to attract the players from their outside options to the intermediated trade. If the trade is to take place (i.96
Handbook of Quantitative Supply Chain Analysis
and πb (v1 ) = πs (s2 ) = 0.
. we simply deﬁne the condition Θ(Ψb (v). For instance.) are monotone increasing functions in [v1 . in the above example.

6. from the viewpoint of supply chain intermediation. The intermediary makes a proﬁt by creating a nonzero bid-ask spread which clears the market.g. an eCommerce site. In this setting. there is no preestablished supply structure. We now turn our attention to multilateral trades. The trade under consideration consists of one par-
. a pre-established supply chain structure dictates the set of suppliers a wholesaler deals with.. the intermediary creates value by devising efﬁcient mechanisms that help the supplier to elicit willingness to pay information from the buyers and to identify the most lucrative trade. quality. First. the model associated to matching markets is directly linked to the bilateral bargaining model.
Multilateral Trade with Incomplete Information
Our analysis has so far focused on the role of intermediary in bilateral bargaining situations. In Section 6. we characterize the role of an intermediary in multilateral trade with markets using the framework by McAfee (1992). In Section 6. in a buyer-centric environment. and product speciﬁcations). or the set of retailers a supplier sells to. this multilateral trading environment is directly linked to the bilateral bargaining framework established before. At any one time.2. a supplier may face a particular set of buyers. Similarly.. In this setting. a procurement auction) and the intermediary functions as a coordinator of the exchange. we consider a supplier facing m buyers so that M = (1. m). we characterize multilateral trade with vertical integration using the basic framework of Myerson (1981) and Bulow and Roberts (1989).. Similarly..1
Multilateral Trade with Vertical Integration
In this section. Without the lost of generality. the intermediary may devise mechanisms that help the buyer to elicit cost information from a preestablished set of suppliers. the buyers and suppliers come to a central exchange (e. A matching market emerges since it may be costly for the buyers and the suppliers to seek out each other directly.. delivery date).g. there are costs involved in setting up a central place (e. we characterize the role of intermediary in multilateral trades where one supplier faces multiple buyers or one buyer faces multiple suppliers. in a vertically integrated setting. .. In the supply chain. The intermediary creates value by continuously shaping the portfolio of suppliers (customers) that best match the needs (market potential) of the customers (suppliers). We will show that from the perspective of supply chain intermediation. What is left to be determined is the particular term of trade (e. multilateral trade could occur in at least two different settings. quality. price.g. communication of price. However. infrastructure costs) and there are variable costs associate with the transactions (e..1. The second setting is in a matching markets. identifying the most desirable supplier for the trade.g.Supply Chain Intermediation
97
6.

Let Γ(β. and other bidders j = i valuations in terms of gj (vj ) buyer i’s expected gain from the trade is as follows: πi (β. knowledge of her own valuation vi . vm ). expected seller (supplier) revenue is maximized if the seller announces a certain reserve price (the minimum bid she would accept). w). it is sufﬁcient to consider an incentive compatible direct mechanism that will carry out the trade. All players are inﬂuenced by other buyers’ valuations. As before..37) gi (vi ) Since the supplier’s opportunity cost s is known. vi+1 . p. w) represents the direct revelation mechanism. They show that this reserve price is independent of the number of buyers and it is strictly greater than the supplier’s opportunity cost s. the supplier reports her opportunity cost s. To the intermediary. It may be convenient to think that the intermediary determines a reserve price for the object at us (v). . The supplier’s opportunity cost s is common knowledge. . Each buyer i holds private information about her valuation vi ∈ [ai . Myerson 1981. vi ) =
T−i
(ui (v)βi (v) − pi (v))g−i (τ−i )dτ−i
(3.98
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ticular bundle of goods and services that can be considered a single object. p. the intermediary holds a vector of value estimates v = (v1 .f. Given mechanism Γ(β. However. p.vi−1 . among all possible mechanisms. Milgrom and Weber 1982). one that would maximize her expected net revenue.. This perspective is useful in that it helps us to deﬁne the role of the intermediary in the one-supplier. and each buyer i reports her valuation vi . This problem has been examined extensively in the context of optimal auctions (c.. The intermediary establishes the buyer’s virtual willingness to pay Ψi (vi ) as follows: 1 − Gi (vi ) Ψi (vi ) = vi − (3.. Maskin and Riley 1984.38)
. Thus. Myerson (1981) proposes the optimal auction design problem: the supplier chooses... and she submits a bid of us (v) such that if none of the bids received from the buyers are above us (v). the intermediary establishes the supplier’s opportunity cost Ψs (s) = s. multiple-buyer setting.. where βi (v) is the probability that buyer i will get the object. bi ] that is known to the others in the form of distribution function Gi (vi ) and density gi (vi ). and w(v) is the expected payment from the intermediary to the supplier. vm ) for other buyers.. pi (v) is the expected payment from buyer i to the intermediary. the intermediary may announce a reserve price us (v) based on her knowledge of the vector v and that us (v) ≥ Ψs (s) = s. Each buyer i holds a vector of value estimates v−i = (v1 . which result in a quasi-linear valuation ui (v) for each buyer i. The intermediary faces a mechanism design problem with the goal of eliciting buyers’ willingness to pay for the object. the intermediary keeps the object (the trade fails to take place). . Riley and Samuleson (1981) shows that for a broad family of auction rules..

1−Gi (vi ) = q. vi ’s are draw from independent. Bulow and Roberts (1989) offers an insightful interpretation of virtual willingness to pay as follows. buyers whose willingness to pay vi < us (v) has no incentive to participate in the trade.. Using the above interpretation.e. and the Y axis as value v. While the above model was developed in the context of auction optimization. Moreover. An important insight from the above analysis is that the intermediary matches the supplier with the buyer with the highest virtual willingness to pay. The buyer’s revenue is qvi . This is because Myserson’s model assumes asymmetric buyers (i. there are m independent markets. Bulow and Roberts (1989) show that Myerson’s optimal auction problem can be described as the third-degree monopoly price discrimination problem where instead of m independent bidders. the intermediary offers the object to the buyer with the highest virtual valuation Ψi (vi ) so long as it is above the reserve price. Since the intermediary only need to pay the supplier her opportunity cost s. This represents the buyer’s demand curve.3). i.. Gi (bi ) = 1) (see Figure 3.37). the buyer’s marginal revenue is identical to her virtual valuation Ψi (3. which may not be the buyer with the highest willingness to pay. The monopolist allocates the object(s) to the
. the intermediary may screen out buyers by setting the reserve price. we may compute the buyer’s marginal revenue as follows. where us (v) represents her knowledge of the market. Thus.e. In setting up the reserve price.100
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In other words. Similar to the bilateral bargaining case.. For each buyer i. the intermediary may be thought of as a buyer with a value and marginal revenue of zero. she could generate proﬁt from the difference (us (v) − s). i. dq · vi dq = dqG−1 (1 − q) i dq
dG−1 (1 − q) i dq q −1 = Gi (1 − q) − −1 gi (Gi (1 − q)) 1 − Gi (vi ) = vi − gi (vi ) = G−1 (1 − q) + i Clearly. but not necessarily identical distributions). graph the inverse of her cumulative distribution function Gi (where Gi (ai ) = 0. where vi = G−1 (1 − q). it provides a general framework of analysis for multilateral trade with vertical integration.e. the intermediary offers the object to the buyer with the highest marginal revenue so long as it is positive (above her own). the intermediary plays the important role of regulating the trade such that it is proﬁtable. Deﬁne the X axis as the probability that the buyer’s value exceeds a certain value. From the demand curve for each i buyer.

We introduce a multilateral trading model that captures the basic essence of intermediation in an exchange setting. From the above discussion. It is the common believe of all traders that each buyer’s value is
. in the context of bilateral bargaining with incomplete information (5). Moreover. showing that Ψb and Ψs are equivalent to the buyer’s marginal revenue and the supplier’s marginal cost. The only crucial assumption being made here is that marginal revenue is downward sloping in quantity within each market.18).3. and each supplier j has a privately known cost sj for the good she sells. There are m buyers and n suppliers. each buyer i has a private valuation vi for a single unit of good. and both can be interpreted in the context of pricing problem in microeconomics theory.Supply Chain Intermediation
vi .
6.2
Multilateral Trade with Markets
In this section. Thus. respectively. (1989)
1
q ≡ 1 − Gi (vi )
Interpretation of the Bidder i’s Virtual Willingness to Pay (Bulow and Roberts
buyer(s) with the highest marginal revenue. the intermediary’s function is to make sure the trade only takes place when the (buyer’s) marginal revenue is greater than the (supplier’s) marginal cost. MRi
101
b1 Demand Curve
vi = Gi−1 (1 − q)
MR Curve
MRi (vi ) = vi − 1 − Gi (vi ) g i (vi )
a1
0
Figure 3. we further extend the insights derived from bilateral bargaining in a multilateral setting.17) and the supplier’s virtual opportunity cost Ψs (3. Bulow and Roberts (1989) offer a similar interpretation for the buyer’s virtual willingness to pay Ψb (3. it is interesting to note that the theoretical underpinning of multilateral trade is directly linked to the bilateral bargaining situation.

A well known form of trading in this environment is a call market. The intermediary determines the market clearing price p0 as follows: 1 p0 = (v(k+1) + s(k+1) ) 2 (3. (1994) models the call market as a k-double auction.. constructs supply and demand curves. Hagerty and Rogerson (1985) discusses a ﬁxed-price mechanism where trades occur among buyer and sellers who indicate their willingness to trade at a ﬁxed-price p∗ . the suppliers report their opportunity costs and are ranked as s(1) ≤ s(2) . ≤ s(n) . all trades are made at a single market clearing price. we deﬁne v(m+1) = sup{v : G(v) = 0} (the lowest possible value) and s(n+1) = inf {s : F (s) = 1} (the highest possible cost). Similarly. In the following. Trades occur among buyers who bid at least p0 and sellers who offer no more than p0 . Wilson (1985) initiated the study of double auction as a means to model multilateral trading with incomplete information. 1] deﬁnes a speciﬁc mechanism. McAfee (1992) proposes a double auction model that explicitly considers the role of an intermediary who intervenes in the trade and keeps track of supply and demand at asked and bid prices. Step 1.. In such a double auction. ≥ v(m)) . b] from which a market clearing price p0 is deﬁned as p0 = (1 − k)a + kb. determines a market-clearing price. Several mechanisms have being proposed to model the call market. Like the market specialist in NYSE. Where index (i) represents the ith highest valuation buyer or the ith lowest cost supplier. Step 2. and each supplier’s cost is distributed according to F (s). The intermediary ﬁnds the efﬁcient trading quantity k ≤ min m. n satisfying vk ≥ sk and vk + 1 < sk + 1. Myerson and Satterthwaite (1983). the intermediary makes a proﬁt by regulating the trade using a certain mechanism. where the buyers’ bids and the suppliers’ offers are aggregated to form (discrete) supply and demand curves. The crossing of their graphs determines an interval [a. Rustichini et al.. who ranks them as v(1) ≥ v(2) ≥ . In a call market. and Gresik and Stterthwaite (1989) he shows that a sealed-tender double action is incentive efﬁcient if the number of traders are sufﬁciently large.. we describe this double auction as a direct revelation mechanism.102
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distributed according to G(v).46)
. the intermediary collects bids from the buyers and offers (asks) from the suppliers. Extending the results from Myerson (1981). with traders on the long side of the market randomly given the right to 0 trade. The buyers report their willingness-to-pay to the intermediary. which describe the basic operation of the New York Stock Exchange (NYSE). Step 3. The choice of k ∈ [0. Further. and executes the trade.

In addition to coordinating the multilateral exchange. but with multiple buyers and sellers. the intermediary sets up a central place for the suppliers and buyers to trade. McAfee (1992) shows that for the direct mechanism described above.4). The price is raised continuously. she is dropped out of the auction. All bidders are active at price zero. the k − 1 highest value buyers and trade with the k − 1 lowest cost suppliers. This is important as it eliminates the needs to consider strategic behavior of the traders. and (2) preventing the least proﬁtable trade (the trade between the lowest value buyer and highest cost seller) from taking place. Otherwise. all buyers and suppliers (1) through (k) trade at the market clearing price p = w = p0 . The simple model above describes the main role of the intermediary in multilateral trading. This selection process occurs naturally in the above mechanism as only (up to) k most efﬁcient trades take place between the most compatible pairs of suppliers and buyers.Supply Chain Intermediation
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Step 4. McAfee (1992) proposes an oral double auction work in a similar fashion. and the intermediary keeps the total bid-ask spread (k − 1)(p − w). and a bidder who wishes to remain active at the current price must depress a button. which is the a complication found in the double auction analysis. When she releases the button. it is a dominant strategy for the traders to truthful reporting their valuations. The intermediary sets bid and asked prices to maximize proﬁt and balances the purchases and the sales. After any bidder withdraws. the auction ends.e. The intermediary makes zero proﬁt (p − w = 0). buying at the asked price w = s(k) and selling at the bid price p = v(k) . i. the intermediary designs (bidding) mechanisms for customers and suppliers that reveals their willingness to pay levels and opportunity costs.. As mentioned above. The above selection function can be further illustrated by the oral double auction described in McAfee (1992). where buyers pay p = v(k) and suppliers receive w = s(k) . if p0 ∈ [s(k) . To execute the market with budget balanceness. v(k) ]. Milgrom and Weber (1982) describes a variant of the English Auction where the price is posted electronically. All buyers with a below threshold willingnessto-pay level and all suppliers with an above threshold opportunity cost will be excluded from the exchange. thus creating a proﬁt (k−1)(p−w) = (k−1)(v(k) −s(k) .
. In the following. while continuously selecting the portfolio of suppliers (buyers) that best match the needs (market potential) of the buyers (suppliers). No bidders who has dropped out can become active again. we use the oral double auction model to characterize the basic functions of exchange coordination carried out by a market intermediary (see Figure 3. all remaining bidders know the price at which she drops out. When there is only one bidder left in the room. The ﬁnal step is key for the intermediary to maintain budget balanceness while making a proﬁt (sometimes) by: (1) charging the buyers a higher price then the sellers receive.

i. p(t) and w(t) are the bid and asked prices.e. = 0. The trading process completes at the ﬁrst time T when the number of buyers equals the number of suppliers. p(t). Buyers and suppliers enter a central trading space operated by an intermediary. The trades take place. It is a dominant strategy for a buyer with willingness-to-pay of v to remain active in the intermediated trade as long as v > p(t). The intermediary collects the bid price p(T ) from the buyers and pay the asked price w(T ) to the suppliers. n(t).e. where m(t) and n(t) are the number of active buyers and suppliers. w(t)) in continuous time t. w (t) = 1. The above procedure is a stylized implementation of the direct mechanism described earlier. m(T ) = n(T ) p(T ) ≥ w(T ) Step 3. The
. n(0) = n. p(0) = inf {v : G(v) > 0} w(0) = sup{s : F (s) < 1}. At t = 0. The intermediary keeps track of the state of the system (m(t). and the bid price is no less than the asked price.48)
Step 2.
(3.. Suppose there are more suppliers than buyers initially entering the intermediated trade (m ≤ n). An inactive trader can not be active again during the trading process. They only need to decide whether to stay active in the trade or not. = 0. The decision for the buyers and the suppliers are quite simple. and for a supplier with opportunity cost s to stay active as long as s < w(t). the intermediary updates the bid and asked prices based on the number of active buyer and suppliers.. i. respectively. i.e. she raises the bid price at a unit rate if there are more buyers than suppliers. Step 1. she reduces the asked price at a unit rate if there are more suppliers than buyers. if m(t) ≥ n(t) if m(t) < n(t) if n(t) ≥ m(t) if n(t) < m(t)
(3. The intermediary keeps the difference m(T )(p(T ) − w(T )). Speciﬁcally. p (t) = 1. m(0) = m. At any time t during the trading process. thus become inactive. and the bid and asked prices are set at the most favorable levels..47)
The buyers and suppliers may choose to leave the trading space anytime during the process.104
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Step 0.

Similarly. If a supplier leaves.
7. It is possible that a buyer’s demand can be met by the a subset of suppliers. The trading process now continues with the equal number of buyer and suppliers.4. They further examine the case where demand is indivisible.Supply Chain Intermediation
Price
105
v(1)
As w) d( ke
Supply
s(k+1) v(k+1)
Bid (p)
s(1)
k
Demand Quantity
Figure 3.
Related Work in the Supply Chain Literature and Research Opportunities
In this chapter. Kalagnanam et al. but p(t) < w(t). and vice versa. In this case. In the context of industrial procurement. We propose to look at the problem of supply chain coordination
. In this way. the gap between ask and bid prices decrease until p(t) ≥ w(t). if a buyer leaves. Our goal is to complement the view offered by the supply chain contracting literature that uses long-term coordination contracts as a primary mechanism to achieve channel efﬁciency. For an overview of various aspects of combinatorial auction such as this. asked prices freeze and bid prices rise until a buyer leave.
Oral Double Auction Proposed by McAfee (1992)
asked price decreases until n − m (highest cost) suppliers drop out. please refer to Chapter 7. The general settings of the double auction assume that any supplier can be matched with any buyer. (2000) propose a double auction mechanism allowing additional “assignment constraints” that specify which bids can be matched with which asks. They propose efﬁcient network ﬂow algorithms to ﬁnd the market clearing allocation which satisﬁes the assignment constraints. ﬁnding the market clearing allocation requires the solution of a combinatorial optimization problem. bid prices freeze and asked prices decline until a supplier leaves. we explore a modelling paradigm for supply chain coordination using the notion of supply chain intermediary.

We introduce four basic settings: bilateral bargaining with complete information. an arbitrator. Chod and Rudy (2003) consider a situation where two ﬁrms unilaterally decide on the investment levels on resources (capacity or inventory) based on imperfect market forecasts.e. or disintermediation may be unavoidable. An informational intermediary alleviates the effects of information asymmetry by serving as a broker. A steam of research has appeared in the supply chain literature which also considers the use of bargaining theoretic models to expand the view of negotiation and coordination in the supply chain. Thus. This theoretical connection establishes a convenient analytical framework for the study of supply chain intermediaries. we consider the intermediary a proﬁt-seeking entity. and auctions to facilitate her coordination/arbitration functions. multilateral trade with vertically integration. trades where the surplus is insufﬁcient to cover the incentive costs and/or the transaction cost may not take place at all. the ﬁrms update their forecasts and they have the option to trade excess resources. they may choose to do so directly or through some form of intermediation.106
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somewhat differently: for any subset of players in the supply chain who desire to establish supplier-buyer relationships. Each setting captures a different aspect of transactional/informational intermediation. bilateral bargaining with incomplete information. alliances. after providing the players proper incentives to participate and to truthfully reveal their private information. When an intermediated trade is unproﬁtable. and multilateral trade with markets. A transactional intermediary improves operational efﬁciencies by serving as an intermediate supply chain player or as a third party service provider. To streamline the thinking.. coalitions. This provides an unambiguous way to divide the system surplus generated from coordination. Chod and Rudy (2003) formulate this problem as a non-cooperative stochastic investment game in which the payoffs depend on an embedded Nash bargaining game. As new information becomes available. one may infer that either an alternative form of intermediation is needed. the intermediary keeps the remainder of the system surplus (if non-negative). or a mediator. An intermediary utilizes a variety of mechanisms such as bilateral contracts. the direct-mechanism framework introduced in the context of bilateral bargaining with incomplete information forms the basis for multilateral analysis. i. One may consider an intermediary’s “proﬁts” as the performance measure of an intermediated trade. We establish the analysis of supply chain intermediation using a bargainingtheoretic framework. As we have demonstrated in the chapter. thus the study of supply chain coordination. the intermediary’s proﬁt is the net surplus from trade minus the transaction costs she has incurred. Deng and Yano (2002) consider the situation where a buyer ﬁrst orders from the supplier (at the contracted price) before market demand is observed. then places additional orders (at the
. Since we allow the intermediary to call off the trade.

while the supplier’s investments (in quality. They shown that this “renegotiation” could signiﬁcantly increases system proﬁt if it is anticipated in the supply contract. Plambeck and Taylor (2002) consider the situation where two OEMs sign quantity ﬂexible (QF) contracts with the CM before they invest in the innovation. Van Mieghem (1999) considers two asymmetric ﬁrms. The OEMs may outsource their productions to an independent contract manufacturer (CM).Supply Chain Intermediation
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spot price) after the demand is observed. He argues that ex ante contracts may be too expensive or impossible to enforce. the manufacturer may purchase some of the excess capacity from the subcontractor. competitive newsvendor problem. and the negotiation of the outsourcing contract is modelled as a bargaining game. court-enforceable contracts. the negotiation sequence. price-setting OEM’s are investing in demand-stimulating innovations. who invest non-cooperatively in capacity under demand uncertainty. where n suppliers are selling complementary components to a buyer (an assembler). 1988 where the play-
. and the coalitional structure. They propose a three-stage game: the suppliers form coalitions. Instead of formal. They show that the bargaining outcome induces the CM to invest in the system-optimal capacity level and to allocate capacity optimally among the OEMs. Nagarajan and Bassok (2002) consider a cooperative. then the coalitions negotiate with the assembler on the wholesale price and the supply quantity. These relational contracts are analyzed in as a repeated bargaining game where the buyer’s demand and the supplier’s capacity are private information. multidimensional. and technology innovation) may be non-contractible. IT infrastructure. They show that the players’ bargaining power regarding the spot prices depends upon the outcomes of demand. Plambeck and Taylor (2001) consider the situation where two independent. They show that joint efﬁciency can be achieved through the bargaining process. Thus. the three parties (two OEMs and the CM) bargain over the allocation of this capacity. they study informal agreements that are sustained by repeated interaction. the order quantity and its corresponding price (discount) are determined through seller-buyer negotiation. multilateral bargaining game in a supply chain. After demand is realized. They consider the setting of the spot price the result of a bargaining process. a subcontractor and a manufacturer. Instead of the typical setting where the seller dictates the quantity discount scheme. and they study the effect of bargaining power on the bargaining outcome. Kohli and Park (1989) analyze quantity discounts as a cooperative bilateral bargaining problem. They show that each player’s payoff is a function of the player’s negotiation power. the coalitions compete for a position in the bargaining sequence. Taylor and Plambeck (2003) argue that writing binding contracts that specify the price (and possibly capacity) prior to the supplier’s capacity investment may be difﬁcult or impossible. In case the CM has excess capacity after the demands are observed. In a subsequent paper. he analyzes incomplete contracts Hart and Moore. He models the problem as a multivariate.

. the viewpoints offered by the supply chain intermediary theory and the bargaining theory could potentially broaden the scope for supply chain coordination. Ertogral and Wu 2001) bargaining games could be used to model the negotiation involved in splitting the channel surplus. it is signiﬁcantly more challenging when the players’ outside options (therefore bargaining power) are deﬁned endogenously as private information. a supply chain player’s bargaining power ultimately determines the offers she receives from the intermediary. buy-back. While it is quite straightforward to incorporate outside options in the complete information setting (as shown in Section 4). (2001) consider a decentralized distribution system with n independent retailers. The bargaining theory and the intermediary theory suggest that the mechanism offered by the intermediary reﬂects supply chain players’ bargaining power. and new insights could be gained on the actual division of system surplus. QF. They propose a cooperative inventory allocation and transshipment mechanism that induces the retailers to choose the Nash equilibrium inventory levels that maximize the system proﬁt.f. Most supply chain contracts split the channel surplus arbitrarily. Bargaining theory offers a generalized view of the negotiation process. Moreover.. Nagarajan and Bassok 2002) and non-cooperative (c.. In any case. Both cooperative (c.. One would expect that the power structure is reﬂected in the bid-ask spread set by the wholesales and distributors. After demand is realized. a supply chain intermediary may devise a mechanism (e. it might be interesting to model the signaling game during the negotiation process where the players choose to reveal a certain portion
. which invariably favor the channel-leader who designs the contract. the retailers bargain cooperatively over the transshipment of excess inventories to meet additional demands. proﬁt-sharing) could be examined based on the players’ bargaining power. taking into account the inﬂuence of bargaining power on the division of systems surplus. As discussed throughout the chapter. post a bid and an asked prices) and eliminates the need for bilateral bargaining (contract negotiation) to actually taking place. Facing stochastic demands. Supply Chain Coordination and the Division of Surplus . In the following. Each retailer chooses her own inventory level based on a certain stocking policy.g.f. In other words.g. Anupindi et al. thus the share of the system surplus she receives. Modelled as a bilateral bargaining game.108
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ers leave some contract parameters unspeciﬁed ex ante while agreeing to negotiate ex post. Suppose a supply chain has a retailer signiﬁcantly more powerful than the manufacturers. we outline a few research opportunities offered by the proposed paradigm. the incomplete contract allows the consideration of the player’s bargaining power. A variety of supply contracts in the literature (e. the retailers may hold stocks locally and/or at centralized locations.

and sourcing strategies. the manufacturer ﬁlls customer orders directly without going through intermediaries such as the retailers and distributors. Strategic Supply Chain Design . In fact. quality level. i. and assessing the impact of different intermediation strategies to overall supply chain efﬁciency. The demand sharing process may be described as a simple signaling game as follows:
.. Computing Baysian-Nash equilibrium under these conditions are known to be very challenging. the OEM may have to address issues such as the following: How to conﬁgure transactional intermediaries who could support the growth of both traditional and Internet channels? How to conﬁgure informational intermediaries who could overcome information asymmetry (e. disengaging existing intermediaries. demand. supply chain partnership agreements are typically built on the basis that the buyer desires favorite pricing and responsive supply. The design of such informational intermediation presents signiﬁcant research opportunities. pricing) across and within the channels? How to reintermidate exiting intermediaries in the traditional channel for the integrated channel? What incentives are there to facilitate the transition from traditional to integrated channels? The above example represents opportunities to study strategic supply chain design focusing on placing new intermediaries. third party distribution channel for her electronic products. For instance. the auditor is an informational intermediary who alleviates the inefﬁciency due to asymmetric information. In order to integrate the traditional and the Internet channels. Suppose the supply chain partners are to develop a joint demand management process. Intermediary to foster Information Sharing . As suggested earlier in the chapter. the success of any supply chain partnership hinges on the intermediation mechanism used to handle information sharing.e. Suppose a high-tech OEM has a traditional.. However. but there is information asymmetry since only the buyer can observe the demand. The OEM is interested in developing an Internet channel incorporating the drop-shipping model. The need for information intermediation arises when supply chain players recognize their limited abilities to share information.Supply Chain Intermediation
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of their outside options at a certain point in time during the negotiation. we may take the viewpoint of a supply chain integrator who uses intermediaries as a strategic tool to improve overall supply chain design. as discussed earlier in the chapter.g. the players may not want to share private information such as pricing. thus a third party auditor is typically called in to monitor the partnership. In this context. evaluating the interdependencies of intemediation/disintermeidation. while the supplier wants improved demand visibility and stability.

contract manufacturers in the high-tech industry such as Solectron. Thus. (4) The buyer and the supplier each receives a payoff as a funcˆ tion of dt . and she expects to transact with many buyers and suppliers over time. This signaling game is a dynamic game with incomplete information. The game repeats for each period t. the buyer chooses to transact with an intermediary when the expected cost of searching and bargaining in the matching market exceeds the intermediary’s offer. In the latter case. Designing an informational intermediary in this context involves the selection of a payoff function. dt . in which case she searches and meets the supplier directly and bargain over the price and (2) transacting through an intermediary who offers a bid-ask spread by aggregating price/capacity information from many buyers and suppliers. (2) the ˆ buyer observes dt and then choose a message dt for the supplier. the buyer transacts with the intermediary who offers the most attractive price/performacne trade-off. In general. the intermediary may be able to increase the probability of a successful trade since she possesses aggregated information concerning the buyers and suppliers in the market. the buyer may get to choose from competing intermediaries who offer alternative price/performance tradeoffs. and kt . and Celestica maybe considered emerg-
. Rubinstein and Wolinsky.e. or the buyer’s demands may not be sufﬁcient to justify the supplier’s investment on capacity. Similar to the bilateral bargaining game with incomplete information. a buyer must choose from (1) entering the matching market. 1987.. and it is known that the perfect Bayesian equilibrium outcome leads to inefﬁciency.f. a demand signaling scheme. it is possible to develop a direct mechanism such that it is incentive compatible and individually rational for the players to align their demand signals thus avoiding adverse selection.. Gehrig 1993). Given the choice. For instance.110
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(1) Nature draws demand dt for period t from a distribution D. Flextronics. i. When the buyer bargains directly with a supplier in the matching market. and a fundamental understanding of the players’ behaviors under perfect Bayesian equilibrium. The general setting described here allows us to study the microstructure in emerging supply chain environments. When the buyer enters an intermediated trade. markets where the supplier and buyer meet directly without any form of intermediation. the bargaining may breakdown since the supplier’s capacity may not be sufﬁcient to accommodate the buyer’s demands. Emerging Supply Chain Microstructure It is beneﬁcial to broaden the view of multilateral trade from the discussion in Section 6 to consider the case where the intermediary competes with a direct matching market (c. (3) The ˆt (but not dt ) and use it to determine the production supplier observes d level kt .

therefore. By consolidating demands from different OEMs. leading to a challenging and dynamic research problem. On the other hand.Supply Chain Intermediation
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ing intermediaries between the the brand-carrying OEM such as HP. Dell. Thus. contract manufacturers are able to enjoy economies of scale from upstream suppliers. and Nokia and the upstream supply chain capacity. As a result. these contract manufacturers are able to realize a much higher utilization on their equipment and. reduce the unit costs. and by investing and developing highly ﬂexible processes. the price/performance proﬁle of a contract manufacturer changes over time as the technological life-cycle marches over time. the contract manufacturers must compete with one another on different price/performance tradeoffs. However. the contract manufactures are intermediaries who could offer the OEMs greater variety of products at a signiﬁcantly lower cost. by consolidating the component procurement for different customers. while offering the component suppliers greater stability in their demands. The key for a contract manufacturer’s competitiveness is in her ability to sustain highly ﬂexible processes in a dynamically changing environment of technological innovations.
.